Biochemical Reactions - A First Look
89
c.
Determine the difference between
and -
q0
when sof is = 0 and v = 600 mL h'1
d.
The ethanol concentration in the liquid effluent from the reactor is measured to 4.2 g L 1. The
inlet concentration is zero. Determine the rate of ethanol production (C-moles L'1
h'1). Also
determine the mole fraction of ethanol in the liquid.
e.
From physical chemistry the following relation is obtained between the liquid mole fraction
x
and the gas phase mole fraction
y.
y<
=
Yix i
^i_
P
(1)
y
i is the activity coefficient,
p
is the total pressure, and ^ is the partial pressure of component
i
in the gas phase, rc“1
is the vapor pressure of ethanol at the system at the system temperature =
78.4 mm Hg at 30° C
The activity coefficient for ethanol in water is quite high. Rarey and
Gmehling (1993) give the value 6.61
for 7, when
0.01 mol mol*1. Assuming that
thermodynamic equilibrium is established between ethanol in the liquid phase and ethanol in the
gas phase determine how much ethanol is being stripped to the gas phase (C-moles L'h"1) when
Vg = vgf = 1.3 L min*1. Compare with the ethanol produced by the bioreaction (question 4). Will
the evaporated ethanol have a significant effect on vs - i.e. will it invalidate the assumption that
Va =Vgf ?
f.
nmoW
is 31.7 mm Hg at 30° C. Assuming that dry air, 20.96 % oxygen is used as feed to the
reactor. What is the difference between v£f and vsdue to water evaporation? Again assume
thermodynamic equilibrium between liquid and gas phase and Yhio ~ 1
• Will the difference
between vs and vafinfluence the answer to question a?
g.
In question 1 the same oxygen transfer rate would be obtained if vgf was 6.5 L min"1
and the exit
partial pressure of 0 2 was 0.1840 atm.
Reconsider the answer to question 6 if we also here use the assumption vg - v£f. The answer to
this question explains why
• One should try to have a significant difference in oxygen pressure between inlet and
outlet.
* The off-gas should be dried before measuring rc02 (Christensen
et al.t
1995)
The present problem is inspired by the experimental investigation of errors in measurement of oxygen
uptake rates and ethanol production rates in bioreactors performed by Duboc and von Stockar (1998).
This reference deserves a careful study as a preliminary to an experimental study of bioreaction rates.
Problem 3.2 Single-cell protein from ethane
The microorganism
Mycobacterium vaccae
is able to grow with ethane as the sole source of carbon and
energy and with NH3 as the nitrogen source. The limiting substrate is ethane, and the yield
- 23.7
gram dry weight per mole ethane.
a.
Except for small amounts of S and P an elemental analysis of dry cell mass is C, 47.4
wt%; N, 8.30 wt%; H, 7.43wt%. The ash content is 4.00 wt%, while the oxygen content
(which cannot be obtained by the analysis) must be found from a total mass balance.